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arXiv · 0906.5094

Using the $Δ_3$ statistic to test for missed levels in mixed sequence neutron resonance data

Declan Mulhall
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Abstract

The $Δ_3(L)$ statistic is studied as a tool to detect missing levels in the neutron resonance data where 2 sequences are present. These systems are problematic because there is no level repulsion, and the resonances can be too close to resolve. $Δ_3(L)$ is a measure of the fluctuations in the number of levels in an interval of length $L$ on the energy axis. The method used is tested on ensembles of mixed Gaussian Orthogonal Ensemble (GOE) spectra, with a known fraction of levels ($x%$) randomly depleted, and can accurately return $x$. The accuracy of the method as a function of spectrum size is established. The method is used on neutron resonance data for 11 isotopes with either s-wave neutrons on odd-A, or p-wave neutrons on even-A. The method compares favorably with a maximum likelihood method applied to the level spacing distribution. Nuclear Data Ensembles were made from 20 isotopes in total, and their $Δ_3(L)$ statistic are discussed in the context of Random Matrix Theory.

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Declan Mulhall. 2009-07-30. Using the $Δ_3$ statistic to test for missed levels in mixed sequence neutron resonance data. https://doi.org/10.1103/physrevc.80.034612

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